MathDB

In a rectangular array of points, with 5 rows and

N

columns, the points are numbered consecutively from left to right beginning with the top row. Thus the top row is numbered 1 through

N,

the second row is numbered

N+1

through

2N,

and so forth. Five points,

P_1, P_2, P_3, P_4,

and

P_5,

are selected so that each

P_i

is in row

i.

Let

x_i

be the number associated with

P_i.

Now renumber the array consecutively from top to bottom, beginning with the first column. Let

y_i

be the number associated with

P_i

after the renumbering. It is found that

x_1=y_2,

x_2=y_1,

x_3=y_4,

x_4=y_5,

and

x_5=y_3.

Find the smallest possible value of

N.

Problem Statement